For a:v = d / Δt 110 = 0.66 / Δt Δt = 0.66 / 110 Δt = 0.006 s the period is: T = 2Δt T = 2*0.006 T = 0.012 s the frequency is the inverse of the period. so: f = 1 / T f = 83.3333333 Hz (about; Hz = 1/s) b. T = 2π√(m/k) being the mass m = 200g = 0.2 kg = 2*10^-1 kg, π = 3.14 (about) and T = 0.012, k is equal to: 0.012 = 6.28√(2*10^-1 / k) 0.012 / 6.28 = √(2*10^-1 / k) 0.00191082803 = √(2*10^-1 / k) 2*10^-1/ k = 0.000003 2*10^-1 / k = 3*10^-6 k = 2*10^-1 / 3*10^-6 k = 6.67*10^-5
now using hooke's law: F = -kx F = - 6.67*10^-5* 3.3*10^-1 F = -2.20x10^-5m F = -0.22 *10^4 N
Extreme temperatures can increase demand for heating and cooling, and the resulting increases in electricity demand can push up fuel and electricity prices.
As the surface is horizontal, the only change in energy will be the change in kinetic energy, as the box comes to an stop after compressing the spring.
As we know that the surface is frictionless also, this change in kinetic energy must be equal to the change in the elastic potential energy of the spring.
So we can write the following equality:
where
and
Simplifying and replacing by the values, we get:
Solving for k:
k = 3594.7 N/m
b)
For this part, we can just apply the same equality, replacing the value of k by the one we got, and solving for the initial speed v:
